**3D Transformation in Computer Graphics-**

In Computer graphics, Transformation is a process of modifying and re-positioning the existing graphics. |

- 3D Transformations take place in a three dimensional plane.
- 3D Transformations are important and a bit more complex than 2D Transformations.
- Transformations are helpful in changing the position, size, orientation, shape etc of the object.

**Transformation Techniques-**

In computer graphics, various transformation techniques are-

In this article, we will discuss about 3D Translation in Computer Graphics.

**3D Translation in Computer Graphics-**

In Computer graphics, 3D Translation is a process of moving an object from one position to another in a three dimensional plane. |

Consider a point object O has to be moved from one position to another in a 3D plane.

Let-

- Initial coordinates of the object O = (X
_{old}, Y_{old}, Z_{old}) - New coordinates of the object O after translation = (X
_{new}, Y_{new}, Z_{old}) - Translation vector or Shift vector = (T
_{x}, T_{y}, T_{z})

Given a Translation vector (T_{x}, T_{y}, T_{z})-

- T
_{x}defines the distance the X_{old}coordinate has to be moved. - T
_{y}defines the distance the Y_{old}coordinate has to be moved. - T
_{z}defines the distance the Z_{old}coordinate has to be moved.

This translation is achieved by adding the translation coordinates to the old coordinates of the object as-

- X
_{new}= X_{old}+ T_{x}(This denotes translation towards X axis) - Y
_{new}= Y_{old}+ T_{y}(This denotes translation towards Y axis) - Z
_{new}= Z_{old}+ T_{z}(This denotes translation towards Z axis)

In Matrix form, the above translation equations may be represented as-

**Also Read-** **2D Translation in Computer Graphics**

**PRACTICE PROBLEM BASED ON 3D TRANSLATION IN COMPUTER GRAPHICS-**

**Problem-**

Given a 3D object with coordinate points A(0, 3, 1), B(3, 3, 2), C(3, 0, 0), D(0, 0, 0). Apply the translation with the distance 1 towards X axis, 1 towards Y axis and 2 towards Z axis and obtain the new coordinates of the object.

**Solution-**

Given-

- Old coordinates of the object = A (0, 3, 1), B(3, 3, 2), C(3, 0, 0), D(0, 0, 0)
- Translation vector = (T
_{x}, T_{y}, T_{z}) = (1, 1, 2)

**For Coordinates A(0, 3, 1)**

Let the new coordinates of A = (X_{new}, Y_{new}, Z_{new}).

Applying the translation equations, we have-

- X
_{new}= X_{old}+ T_{x}= 0 + 1 = 1 - Y
_{new}= Y_{old}+ T_{y}= 3 + 1 = 4 - Z
_{new}= Z_{old}+ T_{z}= 1 + 2 = 3

Thus, New coordinates of A = (1, 4, 3).

**For Coordinates B(3, 3, 2)**

Let the new coordinates of B = (X_{new}, Y_{new}, Z_{new}).

Applying the translation equations, we have-

- X
_{new}= X_{old}+ T_{x}= 3 + 1 = 4 - Y
_{new}= Y_{old}+ T_{y}= 3 + 1 = 4 - Z
_{new}= Z_{old}+ T_{z}= 2 + 2 = 4

Thus, New coordinates of B = (4, 4, 4).

**For Coordinates C(3, 0, 0)**

Let the new coordinates of C = (X_{new}, Y_{new}, Z_{new}).

Applying the translation equations, we have-

- X
_{new}= X_{old}+ T_{x}= 3 + 1 = 4 - Y
_{new}= Y_{old}+ T_{y}= 0 + 1 = 1 - Z
_{new}= Z_{old}+ T_{z}= 0 + 2 = 2

Thus, New coordinates of C = (4, 1, 2).

**For Coordinates D(0, 0, 0)**

Let the new coordinates of D = (X_{new}, Y_{new}, Z_{new}).

Applying the translation equations, we have-

- X
_{new}= X_{old}+ T_{x}= 0 + 1 = 1 - Y
_{new}= Y_{old}+ T_{y}= 0 + 1 = 1 - Z
_{new}= Z_{old}+ T_{z}= 0 + 2 = 2

Thus, New coordinates of D = (1, 1, 2).

Thus, New coordinates of the object = A (1, 4, 3), B(4, 4, 4), C(4, 1, 2), D(1, 1, 2).

To gain better understanding about 3D Translation in Computer Graphics,

**Next Article-** **3D Rotation in Computer Graphics**

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